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n阶行列式的计算方法 - 下载本文

x1??x1?1?x2??x2?1?x3??x3?1?x1?x1?1?x2?x2?1?x3?x3?1?Dn?x12?x1?1?x1n?1?x1?1?x1x1?x1?1?x12?x1?1?2x2?x2?1?2x3?x3?1?xn??xn?1?xn?xn?1?2xn?xn?1?n?1x2?x2?1?n?1x3?x3?1?n?1xn?xn?1??x2x2?x2?1?2x2?x2?1?x3x3?x3?1?2x3?x3?1?xnxn?xn?1?2xn?xn?1?n?1xn?xn?1?

n?1x1n?1?x1?1?x2?x2?1?x3n?1?x3?1?x1?1x1?x1?1??x12?x1?1?x2?1x2?x2?1?2x2?x2?1?x3?1x3?x3?1?2x3?x3?1?xn?1xn?xn?1?2xn?xn?1?

n?1x1n?1?x1?1?x2?x2?1?x3n?1?x3?1?n?1xn?xn?1?把第一个行列式从第1行起依次将第i行加到第?i?1?行;第二个行列式的第i列提取xi?1?i?1,2,,n?,得 xn2xnx3nx1x12Dn?x31x22x2x32x32x3x33???xi?1?x12i?1n1x11x22x21x32x31xn2xn

x1nnx2nx3nxnx1n?1n?1x2n?1x3n?1xnn?n????xi???xi?1????xi?xj?i?1?i?1?1?j?i?n综上所述,我们介绍了计算n阶行列式的9种常见方法,最后指出:计算一个n阶行列式常常有多种方法,有时需要多种方法配合使用,对于给定的n阶行列式,究竟选择何种计算方法最简便,还需在实践中积累经验.

参考文献:

[1] 张禾瑞,郝炳新.高等代数[M].第四版.北京:高等教育出版社,1999. [2] 毛纲源.线性代数解题方法技巧归纳[M].武汉:华中理工大学出版社,2000.





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